Parallel Lines
Lines in a plane that never intersect or touch each other are called Parallel Lines. Here are 2 examples below:
Conditions for Lines to be Parallel
Two lines ‘l’ and ‘m’ are called parallel if:
1) Each point on line m is at equidistant (exactly the same distance) from line l.
2) Line m is in the same plane as line l but they do NOT intersect (they may extend to infinity).
3) They should point in the same direction.
4) When lines m and l are both intersected by a third straight line (a transversal) in the same plane, the corresponding angles of intersection with the transversal are congruent (same).
Mathematical Test for Parallel Lines
Consider the diagram below:
We can say that the two lines above (light orange coloured) are parallel if any pair of following angles:
|
Type |
Condition |
Example |
|
Corresponding Angles |
Equal |
a = e |
|
Alternate Interior Angles |
Equal |
c = f |
|
Alternate Exterior Angles |
Equal |
b = g |
|
Consecutive Interior Angles |
Add up to 180o |
d + f = 180o |
